[R] nonlinear constrained optimization

[Paul Smith]

On Tue, Aug 19, 2008 at 8:35 AM, Chua Siang Li
<siang.li.chua at acceval-intl.com> wrote:
>
>   Hi.  I need some advises on how to use R to find pi (i is the index) with
>   the following objective function and constraint:
>
>   max (sum i)[ f(ai, bi, pi) * g(ci, di, pi) * Di ]
>
>   s.t.  (sum i)[ f(ai, bi, pi) * Di * pi] / (sum i)[ f(ai, bi, pi) * Di ]  <=
>   constant
>
>   f and g are diffentiable.
>   So, I am thinking of optim with method = "BFGS"? But wonder how to include
>   the constraint.
>   I also saw constrOptim but it says for linear constraint only.
>   So, what will be the suitable function to use then?
>   Also, how should I write (sum i) in R?
>   Many thanks and your help is much appreciated.

Up to my best knowledge, R cannot deal with optimization problems with
nonlinear constraints, unless one uses the penalty method. Outside R,
Ipopt and Algencan can solve problems like yours, but one needs to
program in AMPL and/or C/Fortran.

Paul